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Sin²theta + 6 Cos theta - 9 = 0 find the value theta when 0is less than or equal to 360 degree ​

User Dan Story
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\sin^2(\theta ) + 6\cos(\theta )-9=0\implies ( ~~ \underline{1-\cos^2(\theta )} ~~ )+ 6\cos(\theta )-9=0 \\\\\\ -\cos^2(\theta )+ 6\cos(\theta )-8=0\hspace{5em}\stackrel{\textit{let's just for a second make}}{\cos(\theta )=Z} \\\\\\ -Z^2+6Z-8=0\implies 0=Z^2-6Z+8\implies 0=(Z-2)(Z-4) \\\\\\ Z= \begin{cases} 2\\ 4 \end{cases}\implies \cos(\theta )= \begin{cases} 2\\ 4 \end{cases}

now, let's recall that cosine just as sine have a range of -1 and 1 and anything in between, but in this case we have two values, hmmm 2 and 4, those two guys are out of cosine's range, so there are no angles that will meet those cosine values, so we can say, no real solution.

User Kyle Anderson
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